Given the function f(x)=11−xf(x) = \frac{1}{1-x}f(x)=1−x1, find the power series of f′(x)f'(x)f′(x) centered at x=0x=0x=0.
∑n=1∞nxn−1\sum_{n=1}^{\infty} n x^{n-1}∑n=1∞nxn−1
∑n=1∞xn−1\sum_{n=1}^{\infty} x^{n-1}∑n=1∞xn−1
∑n=1∞nxn\sum_{n=1}^{\infty} n x^n∑n=1∞nxn
∑n=0∞xnn+1\sum_{n=0}^{\infty} \frac{x^n}{n+1}∑n=0∞n+1xn